I need to swap the radiator on my 2003 Jetta and the only place I can do it is my driveway with a slight slope. This is a new place and I've never jacked the car up on this driveway, in addition my garage is full of junk so it's my only choice if I want to DIY. I believe the driveway is less steep near the bottom so I would probably do it there.

My driveway slopes both ways from a peak in the center, and I am used to it. It isn't really any more dangerous sloped to the rear like that as long as the wheels are chocked. I would almost prefer that because you will theoretically gain more clearance under the front and there is more weight on the rear end of the car making it a bit more stable.

Personally I would back it up more to gain more room in front of the garage door. I suppose you will be opening the garage door, but you will be working in that area and you will want enough room to lay down under the bumper to get that lower rad hose. If you are going to flush it through the lower rad hose you will be working in that area a lot.

Nice car dude, but you should consider fixing those rusty fenders. I did mine last year and it is much worse underneath than on the surface, trust me.

I would engage the parking brake, jack up the front two tires, place jack stands, and then chock the rear wheels. I just wonder if this is too much of an incline to do safely.

Thanks!

You will be fine on the slope, HOWEVER, One major thing I would change is set your wheel chocks at the rear tires FIRST You then put the car in neutral and let the car roll into your chocks until it stops, then set your parking brake, then you can jack the car up and set it on jackstands. Doing this will greatly reduce the risk of the car shifting/moving while you are jacking it up and/or placing the jackstands.

Agreed with the others, you'll be fine. Also agree with Tman, chock the wheels first, let your car roll into them, then set the parking brake. This way you have the wedged tires in addition to the brakes keeping the car from moving.